Question

Linear Application=27500 2500g represents the balance in your college payment account-The function C(q) =after q quarters.Interpret the Slope in this situation.The balance in this account is [Select an answer at a rate ofSelect an answer VInterpret the Initial Value in this situation.Afterquarters, the balance in this account is $How many quarters will this account pay for?You can pay forquarters before the money in this account is gone.

Answer 1

The form of the linear function is

$y=mx+b$

m is the rate of change

b is the initial amount

Since the given equation is

$C(q)=27500-2500q$

Where C(q) represents the balance in the account after q quarters

Compare the equation by the form of the function above, then

$\begin{gathered} m=-2500 \\ b=27500 \end{gathered}$

Since m is a negative number, then the rate is decreasing

The balance in this account is decreasing at the rate of 2500 dollars per quarter

Since the value of b is 27500, then

After 0 quarters, the balance in this account is $27500

We need to find the value of q when C(q) = 0

Substitute C by 0 in the equation and solve to find q

$0=27500-2500q$

Add 2500q to both sides

$\begin{gathered} 2500q=27500-2500q+2500q \\ 2500q=27500 \end{gathered}$

Divide both sides by 2500

$\begin{gathered} \frac{2500q}{2500}=\frac{27500}{2500} \\ q=11 \end{gathered}$

You can pay for 11 quarters before the money in this account is gone